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<h1><a href="https://archiveofourown.org/works/27670106">The Intelligence Machine</a> by <a class='authorlink' href='https://archiveofourown.org/users/asherall/pseuds/asherall'>asherall</a></h1>

<table class="full">

<tr><td><b>Category:</b></td><td>Nocturnal Academy Series - Ethan Somerville</td></tr>

<tr><td><b>Genre:</b></td><td>Gen, Magic, Mathematics, Nonbinary side character, no beta we meditate like professor abbacus</td></tr>

<tr><td><b>Language:</b></td><td>English</td></tr>

<tr><td><b>Status:</b></td><td>In-Progress</td></tr>

<tr><td><b>Published:</b></td><td>2020-11-22</td></tr>

<tr><td><b>Updated:</b></td><td>2021-01-04</td></tr>

<tr><td><b>Packaged:</b></td><td>2021-05-06 23:27:20</td></tr>

<tr><td><b>Rating:</b></td><td>Teen And Up Audiences</td></tr>

<tr><td><b>Warnings:</b></td><td>No Archive Warnings Apply</td></tr>

<tr><td><b>Chapters:</b></td><td>5</td></tr>

<tr><td><b>Words:</b></td><td>3,645</td></tr>

<tr><td><b>Publisher:</b></td><td>archiveofourown.org</td></tr>

<tr><td><b>Story URL:</b></td><td>https://archiveofourown.org/works/27670106</td></tr>

<tr><td><b>Author URL:</b></td><td>https://archiveofourown.org/users/asherall/pseuds/asherall</td></tr>

<tr><td><b>Summary:</b></td><td><div class="userstuff">
              <p>Six students - each from a different Nocturnal Academy - have gone missing soon after Professor Miller's lectures.</p><p>*will update tags as we go*</p>
            </div></td></tr>

<tr><td><b>Comments:</b></td><td>4</td></tr>

<tr><td><b>Kudos:</b></td><td>2</td></tr>

</table>

<a name="section0001"><h2>1. Unnamed Academy</h2></a>
<div class="story"><div class="userstuff module">
    
    <p class="p1">"And today, we're going to continue working on our element spells!" Professor Charles Miller said. "I'll just be walking around and helping you for our first thirty minutes. Some of you may have drastically different equations than others - rest assured, there are many paths to the same solution. Please raise your hand if you need any help."</p><p class="p1">The class immediately dissolved into a busy place with chitter-chatter for a few minutes before they all fell silent. They were working on creating element-summoning spells - to create a gust of wind, a burst of fire, a lump of dirt, a glass of water. The spells themselves were basic enough for many of them - especially the elementals - but creating the spells was the tricky part. It used some strange combination of math and magick to explain things, allowing them to create even more powerful spells and whatnot. They could have the flexibility to (quite literally) do whatever they wanted when they understood enough of the math behind it.</p><p class="p1">Of course, these students were just high-schoolers with rudimentary knowledge of magick. There wouldn't be anything dangerous here - just some haphazard making of spells that had already been done before.</p><p class="p1">"Very good," he said to one student. She had already made spell-circles for all four spells, and was busy double-checking her work. "There's no need to check your work again - these are some of the best spell-circles I've seen. And I've seen a lot of them."</p><p class="p1">There were two types of spells that they could create: word-spells and spell-circles. Both of them had their pros and cons. Beyond that, the most common sort of magick was movement based. But the easiest things to create were word-spells and spell-circles.</p><hr/><p class="p1">Three weeks later - three weeks after Professor Miller had departed for another school - she had disappeared without a trace.</p>
  </div></div>
<a name="section0002"><h2>2. 2 - Australian Nocturnal Academy</h2></a>
<div class="story"><div class="userstuff module">
    
    <p class="p1">Alice Dibble rushed into Professor Subrette's class. She had spent too long talking to Professor Abbacus about electrons - VSEPR was weird - but that left her sprinting across the school. She dashed into her seat just as the bell rang.</p><p class="p1">"Class," said Professor Subrette, grabbing their attention immediately. "As a higher-level math class, I expect all of you to be interested in our upcoming lecturer. Professor Charles Miller is from the North American Nocturnal Academy. While his lectures are typically aimed at helping struggling math students, he has decided to spend time teaching the upper-level students an entirely different application of math. These lectures are especially useful for anybody taking Arcane Arts; however, anybody else in this class is free to attend them." She paused. "Are there any questions?" A few hands came up. "Ms. Dibble."</p><p class="p1">"What's the different application of math?"</p><p class="p1">"From what I've heard, you'll be using math to create spells. I am not well-versed in this technique; however, he has said that anybody in a calculus class has the ability to succeed in his class. Mr. Andrews?"</p><p class="p1">"Is it after school?"</p><p class="p1">"Yes. Anybody else?"</p><p class="p1">Professor Subrette took a few more questions before they started onto Riemann sums. They made a lot more sense than the previous unit. When class ended, Alice headed back to Professor Abbacus' classroom. School had just ended; she thought she might be able to catch him before he was down in his lab - and there he was. Some scared seventh-years were scurrying out of the classroom.</p><p class="p1">"Professor?"</p><p class="p1">"Dribble. I've already told you-"</p><p class="p1">"No, it isn't that. Professor Subrette mentioned that a Professor Miller is coming to teach a class next week that has to do with using math to create spells. I was wondering if you knew anything about it."</p><p class="p1">"Professor Miller is an uppity-mage who believes that math is the only way to do Magick and that technomancy is a pile of shit."</p><p class="p1">Alice winced. "I meant-"</p><p class="p1">"The field, however, is useful for creating new spells. It's a bit more concrete than trying words and movements in hopes that something might happen. The chance of backfire can be reduced. Creating powerful spells is easier. A lot of mages use it nowadays. Prior to this, we favored thought-based-magick: creating an idea for a spell and channeling our intent into a series of gestures and words to try to make things happen. Many mages still use this technique because it's obvious and doesn't require any mathematical skill. The field is mainly based off of slightly more advanced math classes - there's only so much you'll be able to do with your knowledge of basic Algebra and Geometry. Geometry is a little more useful if you're creating spell-circles, which are akin to sigils. Algebra, on the other hand, does next to nothing. It can only be used to create the most basic of spells - a gust of wind, a movement of an object - things that require hardly any energy. Calculus' use of limits is a bit more precise and is infinitely helpful when it comes to creating more powerful spells." He paused. "But you'll hear most of this in his class."</p><p class="p1">"Thanks, sir!"</p>
  </div><div class="fff_chapter_notes fff_foot_notes"><b>Notes for the Chapter:</b><blockquote class="userstuff">
          <p>i'm making this math/magick stuff up as i go. it isn't well thought out + is more of a side thing to the actual plot that'll start up in a few chapters.</p>
        </blockquote></div></div>
<a name="section0003"><h2>3. 3 - Unknown Location</h2></a>
<div class="story"><div class="userstuff module">
    
    <p class="p1">There were six bodies laid out on the floor, each looking as if they had been frozen in time.</p>
<p class="p1">All he needed was one more.</p>
<p class="p1">One of them twitched.</p>
<p class="p1">He sighed, and took a moment to re-apply the spells. They shouldn't be moving; that was the point of an immobility spell. And it was a good immobility spell - there was some extra work done so that it kept the bodies in the same condition until the spell was removed. They weren't going to die. Yet.</p>
<p class="p1">His machine was going to be <em>brilliant</em>.</p>
  </div></div>
<a name="section0004"><h2>4. 4 - Australian Nocturnal Academy</h2></a>
<div class="story"><div class="fff_chapter_notes fff_head_notes"><b>Summary for the Chapter:</b><blockquote class="userstuff">
            <p>Professor Miller teaches them about spell circles. Alice makes an impression.</p>
          </blockquote></div><div class="userstuff module">
    
    <p class="p1">"Alice, can ya help me with this problem? Carla's mad at me," said Toby.</p><p class="p1">"Hmm . . . oh! Just factor out the 3x, then use the quadratic formula."</p><p class="p1">Toby gave her a blank stare.</p><p class="p1">"Negative b plus or minus the square root of b squared minus four a c, all divided by 2a. See?" She scribbled out work for the rest of the problem. "Didn't you cover this in class?"</p><p class="p1">". . ."</p><p class="p1">Alice sighed and looked at her watch. "I'd berate you about your lack of attention to academics, but I have to go." She started putting her things in her bag.</p><p class="p1">"Wait! Is this right?"</p><p class="p1">She glanced at his paper. "I think so. It's the same way for the rest of the problems. And if you aren't sure about your solutions, you can plug them back in to the equation." She checked her watch again and walked out of the library, then broke into an unsteady sprint. Professor Subrette's classroom was on the opposite side of the school - she was going to be late.</p><p class="p1">Apparently not. There were only three other people in the room; two of them were teachers. The other was a senior that she didn't recognize. She took a seat in the middle of the room and pulled out her computer. Her watch was off - they had a few minutes before they were going to start. She adjusted her watch before getting started on her English work. She had a hundred-word piece of creative fiction due tomorrow. There weren't many guidelines. She still wasn't sure what to write about - a brief moment of daily life? She wrote down a few sentences about running through the corridors between classes before class started.</p><p class="p1">Nine more people came in before the teacher started talking.</p><p class="p1">"Hello. I'm Professor Miller; this is my assistant, Mx. Hampton. They'll help you when we're applying the lesson. But before we get started, I'd like you each to tell me your names, pronouns, and what math class you're taking."</p><p class="p1">Most of them were in one of the Calculus classes. Then there were two people in Linear Algebra - technically a self-study. Alice had considered taking it this year, but figured Calculus would be easier.</p><p class="p1">He rambled about the history of spell creation for a few minutes. There was a lot of trial and error and general randomness for a few hundred years. Then people started working on concrete ways of making spells with intentions and gestures. Since then, they had been working out of thought-based magick, with some sigil and rune work. Those fields had been mostly experimental until fifty years ago, when Professor Miller started using math to create sigils.</p><p class="p1">"In this class, we'll be using spell-circles. They are a type of sigil that draws off of geometry, with a little bit of calculus to ease the way. Just some basic derivative-work so that you can do small spells. They won't seem that important here, but if you continue studying this field, you'll find that derivatives are useful for putting together larger spells. They'll help you prevent mistakes. And in this field, any minor mistake can have major consequences. Channeling what you want the spell to do can sometimes help, but you shouldn't rely on that to solve all of your problems."</p><p class="p1">With that explanation out of the way, he dove into explaining how to make spell circles. Alice continued to scribble down notes, but she didn't feel like she was understanding anything that he was saying. A quick glance around the rest of the room showed her that everybody's head was spinning. Perhaps it would be easier to understand in practice.</p><p class="p1">The chalkboard was filled with content. "I'll give y'all a few minutes to copy this down before we dive into the practical work."</p><p class="p1">The person sitting next to her - Bertrand, she thought - whispered, "Do you understand any of this?"</p><p class="p1">"A little . . . the geometry part is straightforward enough. It's just the derivatives that are lost on me. I think it'll make more sense when we make them, though."</p><p class="p1">"Hopefully . . . I'm not sure why I bothered coming. I might as well be failing Calculus - I fell behind when we were working on the Chain Rule, and never caught up." He smiled. "I understand that bit now, though."</p><p class="p1">"I don't think we're doing much other than the easy derivatives? It depends on what we're making. Hopefully nothing too complicated."</p><p class="p1">Professor Miller clapped his hands. "Alright! We're going to spend the next hour working on element creation spells. You'll be trying to make spell-circles that create - or summon - air, water, fire, and earth. When you think you're done, have me or Mx. Hampton look over your work. We'll be testing them on Friday. Don't feel pressured to make sure that all of them are done by then, though. It's better for you to have one working spell-circle than four that don't do anything. I'll go over activating them tomorrow." He smiled. "While you can work with your classmates, I'd rather that you do most of your own work. No copying!"</p><p class="p1">Alice started working on the wind spell. It seemed like the most straight-forward one - she had to move air, not make something out of nothing. She worked haphazardly for a couple minutes and doodled, then -</p><p class="p1">"Oh! I think I have it," she whispered. She drew a few more things and worked out some of the derivatives to check her work before copying the diagram down on her computer. Spell circles could be used repeatedly - draw once, activate again whenever. She had a feeling that it might be nice to have all of them stored on her computer.</p><p class="p1">The rest of the spells were pretty similar, she realized. All she had to do was change the number of terms that she was dealing with . . . and factor some other things for earth. That was the most complex of the four, since there was a bit more force involved. It was weird, and she wasn't even sure if she was doing it right.</p><p class="p1">Bertrand leaned over. "You're already done? I'm still working on air . . ."</p><p class="p1">She glanced at his work. "You messed up the signs."</p><p class="p1">He stared at his paper for a solid minute - "OH!" - and scribbled down the rest. "Thanks. But it doesn't look at all like yours. Maybe you're wrong," he said, a slight grin on his face.</p><p class="p1">"Actually, your circle seems to be more complicated. You could have just moved air around - that's what mine does."</p><p class="p1">He facepalmed. "Wow, I'm an idiot."</p><p class="p1">"It makes the rest of your spells easier. All you have to do is change the element - actually, if you took your first one with the signs as is, all it would have taken was another line for earth. And that was the hardest one for me."</p><p class="p1">"Alice, Bertrand . . . I see that the two of you are almost done?"</p><p class="p1">"No. Those were just some mistakes with my air circle. Alice is, though. She was helping me figure out the where I went wrong with air."</p><p class="p1">He looked over her computer screen. "Those are all pretty simple. Why?"</p><p class="p1">"I didn't want to make them too powerful. Besides, it's easier to make a weak spell stronger than a strong spell weaker. I would rather not increase my chances of backfire."</p><p class="p1">"Very good. I don't suppose that you would be ready to test them tomorrow? I think they would make a nice demonstration."</p><p class="p1">"Sure?"</p><p class="p1">"Great. If you can show up a few minutes before class tomorrow, I can teach you how to activate them. For now, you're free to go."</p><p class="p1">"Thank you, sir."</p><p class="p1">He walked away.</p><p class="p1">"Bertrand?"</p><p class="p1">"Nah, I think I can handle the rest of them. Bye!"</p><p class="p1">"Goodbye."</p>
  </div></div>
<a name="section0005"><h2>5. Math Classroom, Australian Nocturnal Academy</h2></a>
<div class="story"><div class="userstuff module">
    
    <p class="p1">"Of course you would have already made top of the class," said Carla. "Oh well." She sighed.</p>
<p class="p1">"So do you need me to help you after I get out, or . . ." said Alice.</p>
<p class="p1">"Y'know, I think Milly might be open. She's good enough at Tooth and Claw - a new fighter. Knock their socks off."</p>
<p class="p1">Alice dashed off - she figured being fifteen minutes early would be early enough. Activating spells shouldn't be too hard. She knew some Magick; that should have something to do with activating spell circles . . . and she was the first one their. She let out a sigh of relief - she wouldn't have to put on a show for them just yet.</p>
<p class="p1">"Ms. Dibble? Professor Miller is busy right now, but I can teach you how to activate them," said Mx. Hampton.</p>
<p class="p1">"Er, sure! Just let me get them out . . ."</p>
<p class="p1">They took a few minutes to explain how to activate the spell circles. It was as straightforward as Alice thought.</p>
<p class="p1">"Try air first. The fewer possible disasters, the better."</p>
<p class="p1">Alice did. A gust of uncontrolled air swept across the room. Alice tried it again, thinking about controlling it so that it went where she wanted it to go. It didn't quite work - and then again, when she pretended it was coming out of her palm. That worked.</p>
<p class="p1">"Very good! Now, earth. Same method as air."</p>
<p class="p1">Alice nodded, and held her palm face up. There was a tickling sensation; a small mound of dirt appeared, as if out of nowhere.</p>
<p class="p1">"That's good. Now -" they took out an empty cup "- try to put water in here."</p>
<p class="p1">It took a few minutes to fill the cup halfway.</p>
<p class="p1">"Your spell circle is very controlled - if you raise it to any higher power, it'll be stronger."</p>
<p class="p1">Alice laughed. "Yeah, I was a bit worried about it being too strong . . ."</p>
<p class="p1">"Hey, Alice!" Bertrand said as he walked into the classroom.</p>
<p class="p1">"Hi!" She turned her attention back to Mx. Hampton. "So how do I do fire?"</p>
<p class="p1">"The same way as you did all the others. Given the weakness of your spell circle, there's no reason why it could get out of control."</p>
<p class="p1">Alice took a breath, held out her palm, and muttered: "Fire." A small orange flame appeared in her hand. "Wow, it doesn't even hurt!"</p>
<p class="p1">"Very good."</p>
<p class="p1">"That's really cool! Mx, could I give it a try?" said Bertrand.</p>
<p class="p1">They looked at the clock - five minutes until class would start. Professor Miller wasn't there yet, nor was the rest of the class. "Sure. Just let me see your spell circles."</p>
<p class="p1">He took out a few pieces of paper and handed them to her. "I did some research last night," he said to Alice. "I think that-"</p>
<p class="p1">"Bertrand, right?"</p>
<p class="p1">"That's my name!"</p>
<p class="p1">"These are really powerful. You'll have to wait until Professor Miller finishes his lecture.; they have to be cast outside. Were you looking into weather and natural disasters last night?"</p>
<p class="p1">He laughed. "No, just some reading in the library. I know a bit of Magick myself, so I was looking at how that translated to math. I guess they're a bit stronger than I thought they were . . ."</p>
<p class="p1">Professor Bertrand - and the rest of the class - rushed into the room. "It looks like everybody's late today. To your seats! It's a short lecture today, but I want you all to be able to finish your spell circles."</p>
<p class="p1">"Wow, can I see your equations? After his lecture, I mean," Alice said to Bertrand as they walked to their seats.</p>
<p class="p1">"Sure."</p>
<p class="p1">The lecture was a quick review on what they had learned yesterday, with a little bit of time spent on activation. "We'll talk more about that one-on-one, since it can depend on the spell circle. When you're done, call me or Mx. Hampton over to take a look at your spells. But first, a demonstration! Alice?"</p>
<p class="p1">"Sure." She walked to the front of the class.</p>
<p class="p1">He handed her a piece of chalk. "Draw them on the board, explain your process, and then cast them."</p>
<p class="p1">She sketched out all of her spell circles and explained them as she drew them. "So while the proportions are a bit off -" she had drawn them so that everybody could easily see them "- you can see that I focussed on making sure that they would only have a minor impact. My equations were just fractional exponents, though you could easily modify them to be stronger. And - as you can see from the triangles - I added safeguards so that an increase in power channelled wouldn't change the spell." She paused, then moved through casting them: air, earth, water, fire. "As you can see, the water spell circle might have contained too many safeguards. I'd backfire if I put too much power into it. Fire, on the other hand, was controlled enough that it doesn't even hurt."</p>
<p class="p1">"Thank you, Alice. Everybody else, please work on your circles."</p>
<p class="p1">She sat back down. "Bertrand?"</p>
<p class="p1">"Sure." He slid a piece of paper over.</p>
<p class="p1">"Wow . . . is it the trig functions? I don't think we talked about those."</p>
<p class="p1">"There's a book in the restricted section that breaks down a lot of word slash intention based spells. I can send you my notes, if you want."</p>
<p class="p1">"Yes please." She paused. "You should probably add some safeguards to fire - don't want to burn down the school quite yet."</p>
<p class="p1">"Maybe. More triangles?"</p>
<p class="p1">"Replace your circles with triangles. At least do some of them . . . maybe the border ones."</p>
<p class="p1">"On it."</p>
<p class="p1">He worked for a few minutes; Alice corrected a couple mistakes. (His wind spell circle might have created a tornado.)</p>
<p class="p1">After checking over the rest of the students. Mx. Hampton walked over to the two of them. "Bertrand, you can go and test your spell circles now. Alice can come."</p>
<p class="p1">"Sure!" "Thanks!"</p>
<p class="p1">They walked out of the classroom; there was a conveniently placed door that led outside.</p>
<p class="p1">They walked him through casting them. "Make sure to face away from the school. Alice, step back - if this backfires or something else happens, you do not want to be standing near him.</p>
<p class="p1">"Got it." She took a few steps back. "Go Bertrand!"</p>
<p class="p1">He smiled. "Okay, I'll start with wind. Here goes nothing." He stood for a minute and held out his palm. A gust of air sailed out - the grass lay flat until he cancelled the spell. "Okay . . . was the spell supposed to end on its own?"</p>
<p class="p1">"That would have gone for a few more minutes if you hadn't ended it." They explained why. "Now try Earth. Don't put as much power into it as you did air."</p>
<p class="p1">He gave them a thumbs up, then cast the spell. A pile of dirt - it was the size of a large candle - appeared on the ground.</p>
<p class="p1">"That's good! Do the same for water."</p>
<p class="p1">It rained momentarily; he quickly cancelled the spell.</p>
<p class="p1">"Okay. Try fire, but please put as little energy into it as you can."</p>
<p class="p1">A flame the size of a large water bottle appeared in his hand.</p>
<p class="p1">"That doesn't hurt? Mx, can I go closer to him?"</p>
<p class="p1">"Yes." "Yep! I think you can touch it."</p>
<p class="p1">Alice held out her hand and - very carefully - put a finger near the fire, then stuck it in. "Wow! It just feels warm . . . maybe a bit too warm." She took her finger out.</p>
<p class="p1">"The two of you, wait here. Professor Miller will be out in a few minutes." Mx. Hampton disappeared; Professor Miller came out quickly.</p>
<p class="p1">"Bertrand! Was that your rain?"</p>
<p class="p1">"Yes, sir!"</p>
<p class="p1">"I overheard you talking to Alice about trig functions . . . did you read Jessica Helmworth's book, perchance?"</p>
<p class="p1">"Yeah. I reworked the air spell circle that you saw yesterday using the inverse sin technique he talked about. The rest was -"</p>
<p class="p1">"All inverse trig. I knew Ms. Helmworth at one point - she wrote the book on trig in spell circles. I've always been more of a calculus person myself. I see your fire spell is working just fine - can you cancel it and show me your air and earth spells?"</p>
<p class="p1">"Sure." He recast the spells; they had roughly the same effect as before.</p>
<p class="p1">"Very good! Let's see . . . we're going to spend all of tomorrow on activation. I can let the two of you go early today. Tomorrow, I want the two of you to demonstrate your spell circles - for contrast, Alice. The rest of the class will learn something from seeing both of your spell circles and activation side by side. I'll let the two of you go after that. Thursday and Friday will be on turning cantrips into spell circles, so that'll be something new for the two of you." He clapped his hands. "Alright! Any questions?"</p>
<p class="p1">"No." "Nope!"</p>
<p class="p1">"Then you're dismissed. Have a good day."</p>
<p class="p1">"You too!" "Farewell."</p>
  </div><div class="fff_chapter_notes fff_foot_notes"><b>Notes for the Chapter:</b><blockquote class="userstuff">
          <p>i realized how much i dislike this fic (IT'S TOO LINEAR). so here's a slight plot twist. might speed write the rest of this today just to get it out of my hands.</p>
        </blockquote></div></div>
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